Hey Rainbow, Where’s My Pot Of Gold?

Looking like some spectacular comet,  a rainbow segment arcs over Duluth’s Park Point and Lake Superior last week near sunset. A different reflected rainbow appears on the water. See explanation below.  Photo: Bob King

Rainbows are the coolest. A week ago I left work absolutely bedraggled. But walking out the back door, I was greeted with the fattest, most colorful stump of a rainbow I’d seen in years. The partial bow bent over the Duluth harbor minutes before sunset, which explains why the red is exaggerated compared to the other colors. Sunset light contains fewer blues, purples and greens. They’re scattered away by the dusty air leaving mostly reds and oranges for the rainbow’s palette.

Raindrops act as tiny prisms that bend or “refract” light into separate colors. A concentration of light exits the raindrop  at an angle of 42 degrees. Credit: UW-Stout

Rainbows occur when sunlight is reflected and refracted by millions of raindrops emerging in concentrated bundles that together create the rainbow. With the early morning or late afternoon sun at your back and rain falling somewhere ahead of you, chances are excellent you’ll see one. I’m always on the lookout after a storm has passed and sunlight suddenly breaks over the clouds.

As sunlight passes from air to water, it’s bent slightly, the same way a straw looks bent or broken standing in a clear glass of water. The bent or refracted beam travels through the drop, reflects off its backside and is directed back out the other side. As the instant it leaves the drop, it’s bent again. Since the outgoing rays are concentrated at an angle of 42 degrees relative to the observer, we see a tightly focused bow of brightly colored light.

We’d see a full 360 rainbow if we could get the ground out of the way.  Since sunlight comes out of the raindrop at an angle of 42 degrees from the direction back to the Sun, we see the primary rainbow 42 degrees or about “four fists” high near sunset. Credit: UCAR

Light is composed of every color from violet to red and each color is bent by a different amount. Violet light is bent the most, red the least. Send a beam of white light through a raindrop or prism and it comes out separated into individual colors.

Red is always on the outside of the primary bow because it’s bent the least; violet on the inside because it’s bent the most. To be precise, violets and blues bend at a 40-degree angle, and the reds bend at a 42-degree angle. That’s a difference of two degrees – the width or spread of the primary bow.

A double rainbow with additional or supernumerary arcs inside the primary arc. The shadow of the photographer’s head on the bottom marks the center of the rainbow circle. Credit: Eric Rolph

We only ever see half a rainbow on the ground. Light leaves raindrops in a the form of a complete circle, the bottom half of which is hidden below the horizon. The best we can do is see exactly half that circle when a rainbow occurs close to sunrise or sunset with the sun at the horizon. When the sun is higher, the top of the rainbow drops lower. When it’s about 40 degrees high, only the tippy top of the rainbow arch is visible stretching along the horizon. Have you ever seen one of these?

A more complete circle can sometimes be seen from a mountain or aircraft, and you can make your own complete rainbow using the spray from a garden hose.

Wide view of Duluth’s rainbow shows a partial secondary bow at far right. Raindrops also direct light inside the rainbow causing strands of falling rain to glow orange in the setting sun. Photo: Bob King

There are many variations on the simple rainbow including the fairly common secondary bow, formed when light gets reflected twice inside a raindrop. After two reflections the beam leaves the drop at an angle that puts the secondary atop the primary with its order of colors reversed. If you’ve ever seen the double rainbow, you’ve probably noticed the outer bow is fainter.

Raindrop interiors are perfect reflectors. A portion of the light shoots straight out their backsides. Since light reflects twice to form the secondary bow, more light is lost and the bow is fainter as a result.

Supernumerary arcs on the underside of the primary rainbow. Photo: Bob King

Additional concentric arcs can form beneath the primary bow more than doubling its width. These green and purple fringes are caused by another property of light called diffraction. Since light takes the form of waves with crests and valleys, as multiple beams leave a rain drop, they’re not necessarily aligned. Troughs from one beam can meet waves from another and cancel each other out to create a dark gap. When wave crests overlap they create a bright fringe. That’s what supernumeraries are.

As a kid, my friends and I used to run toward the ends of the rainbow to look for that proverbial pot of gold. We didn’t know that rainbows aren’t physical objects. Nor are they located at a specific distance – they are not out there. Rainbows are sunlight chopped up and reflected back to our eyes by drops of water. Bows from raindrops a few miles away are identical to those that spring from drops a few feet away. The rainbow you see from where you stand is your personal rainbow formed by droplets feeding sunlight to your eyes. If I stand 10 feet away from you I see my own rainbow.

There are reflected rainbows, reflection rainbows, twinned bows and even moonbows. One could do worse in life than chasing rainbows.

Let’s return to the first picture in this article. See the reflection of the rainbow in the water? Since rainbows aren’t real objects, they can’t produce reflections. What appears to be a reflection is really an entirely different rainbow formed by another set of raindrops across a different line of sight. Sunlight refracts through these drops, then reflects off the water and up to your eyes. So yes, the photo shows two rainbows, not one.